On the use of harmonic Ritz pairs in approximating internal eigenpairs
type: Item
instance of: scholarly article
title: On the use of harmonic Ritz pairs in approximating internal eigenpairs
zbMATH Open document ID: 1028.65030
DOI: 10.1016/S0024-3795(01)00480-3
author: Gerard L. G. Sleijpen
author: Jasper van den Eshof
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: The paper concerns real symmetric matrices and focuses on the extraction of a good approximation of an eigenvectors of an internal eigenpair from an iteratively obtained subspace. Harmonic Rayleight-Ritz was proposed in 1991 by \textit{R. B. Morgan} [Linear Algebra Appl. 154-156, 289-309 (1991; Zbl 0734.65029)] and named in 1995 by \textit{C. C. Paige}, \textit{B. N. Parlett} and \textit{H. A. van der Vorst} [Numer. Linear Algebra Appl. 2, No. 2, 115-133 (1995; Zbl 0831.65036)]. In this paper it is compared with refined Rayleigh-Ritz (a block Arnoldi process) in the sense of \textit{Z. Jia} [Linear Algebra Appl. 270, 171-189 (1998; Zbl 0896.65035)], with emphasis on insight rather than on algorithms throughout this paper. Further topics studied for the same purpose are error analysis (a-priori as well as a-posteriori) and the selection of a suitable harmonic Ritz vector with respect to the shift.
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1864793
zbMATH Keywords: real symmetric matrices
zbMATH Keywords: eigenvectors
zbMATH Keywords: internal eigenpair
zbMATH Keywords: refined Rayleigh-Ritz
zbMATH Keywords: block Arnoldi process
zbMATH Keywords: algorithms
zbMATH Keywords: error analysis
zbMATH Keywords: harmonic Ritz vector
describes a project that uses: JDQZ
MaRDI profile type: Publication
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full work available at URL: s0024-3795(01)00480-3
OpenAlex ID: W2004464554
description: scientific article; zbMATH DE number 1864793